alt Hacker News0.x is not that you don't want people depending on it, you just don't want them to come and complain when you quickly introduce some breaking changes. The project is still in development, it might be stable enough for use in "real projects(tm)", but it might also still significantly change. It is up to the user to decide whether they are OK with this.
1.x communicates (to me at least) you are pretty happy with the current state of the package and don't see any considerable breaking changes in the future. When 2.x comes around, this is often after 1.x has been in use for a long time and people have raised some pain points that can only be addressed by breaking the API.
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If you are at the point that other people can use your software, then you should use v1. If you are not ready for v1, then you shouldn't be releasing to other people.
Because this comment, "The project is still in development, it might be stable enough for use in "real projects(tm)", but it might also still significantly change." That describes every project. Every project is always in development. Every project is stable until it isn't. And when it isn't, you bump the major number.
But people will complain, so ex falso quodlibet